Another potential for which the constant-mass Schrödinger equation is exactly solvable and that can be written in terms of the exponential \(e^u\)  is the Rosen-Morse II potential [1]}
\(U(u) = - A(A+1) \operatorname{sech}^2 u + 2B \tanh u, \qquad -\infty < u < +\infty , \qquad B<A^2, \) 
